Many physical systems exhibit patterns of behavior typified by phase transitions: as a "control parameter" varies, the behavior changes between two (or more) distinct stable states or modes. Recently, examples of such phase transitions have been demonstrated in physiological systems. For example, when subjects tap the index fingers of each hand, there are two stable modes: one in which the fingers tap in phase and one in which they tap in counter-phase. These two modes are robust (stable), and the behavior changes from one to the other as tapping frequency is systematically varied. This behavior exhibits a number of features common to phase transitions: each mode is robust to perturbations, there is increased variability when the control parameter (frequency) is near the transition point, and there is hysteresis such that the transition point is different when approached from above versus below (decreasing or increasing frequency). We will investigate oculomotor behavior for similar types of phase transitions. Mathematical modeling in the oculomotor field is quite sophisticated, yet analysis of phase-transition behaviors has not been attempted. The proposed work is thus an attempt to model an aspect of oculomotor behavior that has not been addressed. The modeling proposed here will have value in improving existing models, understanding observed behaviors, and predicting new ones. The research plan consists of three main efforts. First is the analysis of periodic saccades for evidence of multiple stable states, in analogy to the finger tapping work referred to above. Preliminary data suggests that phase transitions may indeed occur in this system: as target jumping frequency increases, saccades change from lagging the target (positive latency) to anticipating the target (negative latency), and there is increased variability near the transition frequency. Work on this system will involve further verification of this effect, examination of hysteresis and the response to perturbations, and formulation of mathematical models (and analysis of existing models) to reproduce the phase transitions. The second effort is a study of the interaction of saccades and the VOR (vestibulo-ocular reflex), looking for modes of coordination between the resulting smooth and fast eye movements as a function of frequency. Finally, we will carry out a survey of other vestibular and oculomotor behaviors and models for those which might exhibit phase transition behaviors. This project is high risk because the oculomotor system may avoid such phase transitions but rather exhibit smoothly graded behavioral changes, making phase transition models inappropriate. The work represents a new direction for the PI because his past work has not dealt with the unique mathematical formulations required for this study.